Question

Gary is using a combination of regular polygonal tiles for his kitchen floor. He begins the tessellation at a vertex by placing two triangles.

Which two polygons should he use to fill up the vacant space at the vertex and make it possible to tessellate the floor?

Answer 1

1 square and a hexagon because 360 – (60 + 60 + 60) = 60 + 120
1 triangle and a hexagon because 180 = 60 + 120
2 hexagons because 360 – (60 + 60) = 2 x 120
2 squares because 180 = 90 + 90

Answer 2

It depends on the angle (or angles) the two triangles make at that vertex. What is certainly true is the the sum of all the angles of the figures at that vertex must equal 360 degrees. But we cannot know what other figures to place there without knowing more about the first two triangles.

Answer 3

I thought the same thing... I think it might be the two hexagons because if they are fitted right they would fill it up